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Local theory of the collocation method for the approximate solution of singular integral equations, I

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Abstract

A new approach for investigating the collocation method for singular integral equations is given. Using Banach algebra techniques and a local principle established by I. Gohberg and N. Krupnik under suitable conditions the convergence of the Lagrange- and Mul thopp-collocation method is proved for one-dimensional singular integral equations and systems of such equations with piecewise continuous coefficients having a countable infinite number of discontinuities.

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Authors and Affiliations

  1. Sektion Mathematik, Technische Hochschule, PSF 964, 9010, Karl-Marx-Stadt

    Peter Junghanns & Bernd Silbermann

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  1. Peter Junghanns
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  2. Bernd Silbermann
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Junghanns, P., Silbermann, B. Local theory of the collocation method for the approximate solution of singular integral equations, I. Integr equ oper theory 7, 791–807 (1984). https://doi.org/10.1007/BF01195867

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  • DOI: https://doi.org/10.1007/BF01195867

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